I have been told that there are companies that will actually pay housing expenses in the UK for people coming from other countries. Is this really true, and about how many of the companies might offer something like this.

In my experience this would tend to be limited to moving existing employees from one country to another. For external recruits I think it is more likely that they get temporary accommodation - say for 4 weeks - while they are setting themselves up. Unless, as Richard says, the job includes accommodation.